Exploiting Exponentials - SubThreshold.com

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Simply applying a voltage at a gate and gives a current that is proportional to $exp{\frac{kV_G}{U_T}}$
We can take the natural log with a diode connected transistor
- n-channel: $V_G = \left[ U_T \ln \left( \frac{I_d}{I_S W/L} \right) + V_S \right] / \kappa$
- p-channel: $V_G = \left[ V_S - U_T \ln \left( \frac{I_d}{I_S W/L} \right) \right] / \kappa$
- Provided it is in saturation, or $\kappa V_G - V_S > 4 U_T$ (for n-channel)

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